Mathematics class 12

A relation R on a non empty set A is an equivalence relation if it is

• Reflexive
• Symmetric and transitive
• Reflexive symmetric and transitive
• None of the othere

Let A={1, 2,3} then the domain of the relation R ={(1, 1), (2,3), (2, 1) }defined on A is

• {1, 3}
• {1, 2,3}
• None of these
• {1, 2}

A relation R in a set A is called ____ relation, if no element of A is related to any element of A

• Universal relation
• Empty relation
• Equivalence relation
• None of the above

Let f:{2, 3,4,5} --> {3, 4,5,9} and g:{ 3,4,5,9} -->{7, 11,15} be the function defined as f(2) =3, f(3) =4, f(4) = f(5) = 5 and g(3) = g(4) = 7 and g(5) = g(9) = 11. Find gof (5)

• 7
• 11
• 15
• None of these

For the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)), what is true about R?

• R is transitive
• R is reflexive
• R is symmetric
• None of these

If R, is a relation in set N given by R = {(a, b) : a = b – 3, b > 5}, then does elements (5, 7) ∈ R?

• Yes
• No

Given triangles with sides T1 : 3, 4, 5; T2 : 5, 12, 13; T3 : 6, 8, 10; T4 : 4, 7, 9 and a relation R in set of triangles defined as R = {(Δ1, Δ2) : Δ1 is similar to Δ2}. Which triangles belong to the same equivalence class?

• T1 and T2
• T2 and T3
• T1 and T3
• T1 and T4

Every relation which is symmetric and transitive is reflexive also. State true or false

• True
• False

If A = {1, 2, 3} and relation R = {(2, 3)} in A. Check whether relation R is reflexive, symmetric and transitive.

• Not reflexive, not symmetric but transitive
• Not reflexive but symmetric and transitive
• reflexive, symmetric and transitive
• Not reflexive, not symmetric not transitive